where \(\kappa _1 \!=\! \frac{M_1}{a} + \kappa _{10}\) , \(\kappa _2 \!=\! \frac{M_2}{b} + \kappa _{20}\) , and \(\tau \!=\! M_3 \)  (notice that torsional stiffness has been normalized to unity). Together with the initial conditions \(D(0) \!=\! I_{6 \times 6}\)  and \(P(0) \!=\! 0_{6 \times 6}\) , we obtain an initial value problem that is solved with MATLAB. If the solution of Equation (REF ) satisfies \(\det (P) \! \ne \! 0\)  for all \(s \in (0,l]\) , then the equilibrium is stable. If \(\det (P) \!=\! 0\)  for some \(s \in (0,l]\) , then the equilibrium is unstable. If \(\det (P) \! \ne \! 0\)  for all \(s \in (0,l)\)  and \(\det (P(l)) \!=\! 0\) , then we cannot conclude the stability and higher order variations of the energy functional need to be considered [1]}, [2]}.
